Noun
Laplace operator (plural Laplace operators)
(mathematics, physics) A differential operator,denoted ∆ and defined on
R
n
{\displaystyle \mathbb {R} ^{n}}
as
Δ
=
∑
i
=
1
n
∂
2
∂
x
i
2
{\displaystyle \Delta =\sum _{i=1}^{n}{\frac {\partial ^{2}}{\partial x_{i}^{2}}}}
, used in the modeling of wave propagation, heat flow and many other applications.
As a result, the velocity potential φ has to satisfy Laplace's equation : where is the Laplace operator (sometimes also written Δ ). Source: Internet
The delta function has only radial dependence, so the Laplace operator (a. Source: Internet
If f is a harmonic function on U, then all partial derivatives of f are also harmonic functions on U. The Laplace operator Δ and the partial derivative operator will commute on this class of functions. Source: Internet